We report new methods for evaluating realistic observing programs that search stars for planets by direct imaging , where observations are selected from an optimized star list , and where stars can be observed multiple times .
We show how these methods bring critical insight into the design of the mission and its instruments .
These methods provide an estimate of the outcome of the observing program : the probability distribution of discoveries ( detection and/or characterization ) , and an estimate of the occurrence rate of planets ( \eta ) .
We show that these parameters can be accurately estimated from a single mission simulation , without the need for a complete Monte Carlo mission simulation , and we prove the accuracy of this new approach .
Our methods provide the tools to define a mission for a particular science goal , for example defined by the expected number of discoveries and its confidence level .
We detail how an optimized star list can be built and how successive observations can be selected .
Our approach also provides other critical mission attributes , such as the number of stars expected to be searched , and the probability of zero discoveries .
Because these attributes depend strongly on the mission scale ( telescope diameter , observing capabilities and constraints , mission lifetime , etc .
) , our methods are directly applicable to the design of such future missions and provide guidance to the mission and instrument design based on scientific performance .
We illustrate our new methods with practical calculations and exploratory design reference missions ( DRMs ) for the James Webb Space Telescope ( JWST ) operating with a distant starshade to reduce scattered and diffracted starlight on the focal plane .
We estimate that 5 habitable Earth-mass planets would be discovered and characterized with spectroscopy , with a probability of zero discoveries of 0.004 , assuming a small fraction of JWST observing time ( 7 % ) , \eta = 0.3 , and 70 observing visits , limited by starshade fuel .